How did you determine the battery is okay and fully-charged? What you are describing is commonly caused by a discharged battery or loose or dirty battery cable connections. Given the additional symptom of stalling while driving, a failed charging system and run-down battery is the best suspect. This sounds like the starter is having problems or the battery needs to be load tested these guides can help us fix it.
https://www.2carpros.com/articles/starter-not-working-repair
and
https://www.2carpros.com/articles/car-battery-load-test
Please run down these guides and report back.
The place to start is by measuring the battery's voltage with an inexpensive digital voltmeter. If it is good and fully-charged, it will measure 12.6 volts. If it is good but discharged, it will be near 12.2 volts. Charge it at a slow rate for an hour, then measure it again. Let me know what you find for battery voltage.
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Wednesday, November 30th, 2016 AT 5:29 PM